Some technical aspects of Cluster Perturbation Theory (CPT) are presented. CPT is an approximation scheme for calculating the oneparticle Green function of the Hubbard model of interacting electrons on a lattice. It proceeds by (i) dividing the lattice into identical clusters and calculating the Green function by exact diagonalization on a given cluster (ii) extending this Green function to the...

We have used an exact diagonalization technique to study the stability of the t − J-Holstein and Hubbard-Holstein models under the influence of the electron-phonon interaction. Previous results have been obtained using frozen-phonon technique or introducing only a few dynamical phonon modes due to the large Hilbert space. To check these results we have done exact diagonalization in a small clus...

A momentum-space approach of the density-matrix renormalization-group ~DMRG! method is developed. Ground-state energies of the Hubbard model are evaluated using this method and compared with exact diagonalization as well as quantum Monte Carlo results. It is shown that the momentum-space DMRG is a very useful numerical tool for studying the Hubbard model and other fundamental models of interact...

We use exact diagonalization to study energy level statistics and out-of-time-order correlators (OTOCs) for the simplest supersymmetric extension $\hat{H}_S = \hat{H}_B \otimes I + \hat{x}_1 \sigma_1 \hat{x}_2 \sigma_3$ of bosonic Hamiltonian $\hat{H}_B \hat{p}_1^2 \hat{p}_2^2 \hat{x}_1^2 \, \hat{x}_2^2$. For a long time, this was considered one systems which exhibit dynamical chaos both classi...